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NASA NTRS1992

A transient FETI methodology for large-scale parallel implicit computations in structural mechanics

Explicit codes are often used to simulate the nonlinear dynamics of large-scale structural systems, even for low frequency response, because the storage and CPU requirements entailed by the repeated factorizations traditionally found in implicit codes rapidly overwhelm the available computing resources. With the advent of parallel processing, this trend is accelerating because explicit schemes are also easier to parallelize than implicit ones. However, the time step restriction imposed by the Courant stability condition on all explicit schemes cannot yet -- and perhaps will never -- be offset by the speed of parallel hardware. Therefore, it is essential to develop efficient and robust alternatives to direct methods that are also amenable to massively parallel processing because implicit codes using unconditionally stable time-integration algorithms are computationally more efficient when simulating low-frequency dynamics. Here we present a domain decomposition method for implicit schemes that requires significantly less storage than factorization algorithms, that is several times faster than other popular direct and iterative methods, that can be easily implemented on both shared and local memory parallel processors, and that is both computationally and communication-wise efficient. The proposed transient domain decomposition method is an extension of the method of Finite Element Tearing and Interconnecting (FETI) developed by Farhat and Roux for the solution of static problems. Serial and parallel performance results on the CRAY Y-MP/8 and the iPSC-860/128 systems are reported and analyzed for realistic structural dynamics problems. These results establish the superiority of the FETI method over both the serial/parallel conjugate gradient algorithm with diagonal scaling and the serial/parallel direct method, and contrast the computational power of the iPSC-860/128 parallel processor with that of the CRAY Y-MP/8 system.

Farhat, Charbel↗
NASA NTRS1982

Some critical questions about deterministic and stochastic adaptive control algorithms

The purpose of this informal paper is to discuss certain robustness issues associated with existing adaptive control algorithms. A modeling framework for incorporating high-frequency unknown dynamics in the adaptive control framework is suggested. Possible fundamental limitations of existing adaptive control framework is suggested. Possible fundamental limitations of existing adaptive control algorithms are also discussed, with emphasis upon their closed-loop stability properties in the presence of unmodeled high-frequency dynamics.

Athans, M.↗
NASA NTRS1991

Robust control of systems with real parameter uncertainty and unmodelled dynamics

During this research period we have made significant progress in the four proposed areas: (1) design of robust controllers via H infinity optimization; (2) design of robust controllers via mixed H2/H infinity optimization; (3) M-delta structure and robust stability analysis for structured uncertainties; and (4) a study on controllability and observability of perturbed plant. It is well known now that the two-Riccati-equation solution to the H infinity control problem can be used to characterize all possible stabilizing optimal or suboptimal H infinity controllers if the optimal H infinity norm or gamma, an upper bound of a suboptimal H infinity norm, is given. In this research, we discovered some useful properties of these H infinity Riccati solutions. Among them, the most prominent one is that the spectral radius of the product of these two Riccati solutions is a continuous, nonincreasing, convex function of gamma in the domain of interest. Based on these properties, quadratically convergent algorithms are developed to compute the optimal H infinity norm. We also set up a detailed procedure for applying the H infinity theory to robust control systems design. The desire to design controllers with H infinity robustness but H(exp 2) performance has recently resulted in mixed H(exp 2) and H infinity control problem formulation. The mixed H(exp 2)/H infinity problem have drawn the attention of many investigators. However, solution is only available for special cases of this problem. We formulated a relatively realistic control problem with H(exp 2) performance index and H infinity robustness constraint into a more general mixed H(exp 2)/H infinity problem. No optimal solution yet is available for this more general mixed H(exp 2)/H infinity problem. Although the optimal solution for this mixed H(exp 2)/H infinity control has not yet been found, we proposed a design approach which can be used through proper choice of the available design parameters to influence both robustness and performance. For a large class of linear time-invariant systems with real parametric perturbations, the coefficient vector of the characteristic polynomial is a multilinear function of the real parameter vector. Based on this multilinear mapping relationship together with the recent developments for polytopic polynomials and parameter domain partition technique, we proposed an iterative algorithm for coupling the real structured singular value.

Chang, Bor-Chin↗
NASA NTRS1991

Microgravity vibration isolation: An optimal control law for the one-dimensional case

Certain experiments contemplated for space platforms must be isolated from the accelerations of the platform. An optimal active control is developed for microgravity vibration isolation, using constant state feedback gains (identical to those obtained from the Linear Quadratic Regulator (LQR) approach) along with constant feedforward gains. The quadratic cost function for this control algorithm effectively weights external accelerations of the platform disturbances by a factor proportional to (1/omega) exp 4. Low frequency accelerations are attenuated by greater than two orders of magnitude. The control relies on the absolute position and velocity feedback of the experiment and the absolute position and velocity feedforward of the platform, and generally derives the stability robustness characteristics guaranteed by the LQR approach to optimality. The method as derived is extendable to the case in which only the relative positions and velocities and the absolute accelerations of the experiment and space platform are available.

Hampton, Richard D.↗
NASA NTRS2011

Robust and Accurate Shock Capturing Method for High-Order Discontinuous Galerkin Methods

A simple yet robust and accurate approach for capturing shock waves using a high-order discontinuous Galerkin (DG) method is presented. The method uses the physical viscous terms of the Navier-Stokes equations as suggested by others; however, the proposed formulation of the numerical viscosity is continuous and compact by construction, and does not require the solution of an auxiliary diffusion equation. This work also presents two analyses that guided the formulation of the numerical viscosity and certain aspects of the DG implementation. A local eigenvalue analysis of the DG discretization applied to a shock containing element is used to evaluate the robustness of several Riemann flux functions, and to evaluate algorithm choices that exist within the underlying DG discretization. A second analysis examines exact solutions to the DG discretization in a shock containing element, and identifies a "model" instability that will inevitably arise when solving the Euler equations using the DG method. This analysis identifies the minimum viscosity required for stability. The shock capturing method is demonstrated for high-speed flow over an inviscid cylinder and for an unsteady disturbance in a hypersonic boundary layer. Numerical tests are presented that evaluate several aspects of the shock detection terms. The sensitivity of the results to model parameters is examined with grid and order refinement studies.

Atkins, Harold L.↗
NASA NTRS1991

Microgravity vibration isolation: An optimal control law for the one-dimensional case

Certain experiments contemplated for space platforms must be isolated from the accelerations of the platforms. An optimal active control is developed for microgravity vibration isolation, using constant state feedback gains (identical to those obtained from the Linear Quadratic Regulator (LQR) approach) along with constant feedforward (preview) gains. The quadratic cost function for this control algorithm effectively weights external accelerations of the platform disturbances by a factor proportional to (1/omega)(exp 4). Low frequency accelerations (less than 50 Hz) are attenuated by greater than two orders of magnitude. The control relies on the absolute position and velocity feedback of the experiment and the absolute position and velocity feedforward of the platform, and generally derives the stability robustness characteristics guaranteed by the LQR approach to optimality. The method as derived is extendable to the case in which only the relative positions and velocities and the absolute accelerations of the experiment and space platform are available.

Hampton, R. D.↗
NASA NTRS1992

Optimal microgravity vibration isolation - An algebraic introduction

Certain experiments contemplated for space platforms must be isolated from the accelerations of the platforms. An optimal active control is developed for microgravity vibration isolation, using constant state feedback gains (identical to those obtained from the Linear Quadratic Regulator (LQR) approach) along with constant feedforward (preview) gains. The quadratic cost function for this control algorithm effectively weights external accelerations of the platform disturbances by a factor proportional to (1/omega) (exp 4). Low frequency accelerations (less than 50 Hz) are attenuated by greater than two orders of magnitude. The control relies on the absolute position and velocity feedback of the experiment and the absolute position and velocity feedforward of the platform, and generally derives the stability robustness characteristics quaranteed by the LQR approach to optimality. The method as derived is extendable to the case in which only the relative positions and velocities and the absolute accelerations of the experiment and space platform are available.

Hampton, R. D.↗
NASA NTRS1999

Reinforcement Learning in a Nonstationary Environment: The El Farol Problem

This paper examines the performance of simple learning rules in a complex adaptive system based on a coordination problem modeled on the El Farol problem. The key features of the El Farol problem are that it typically involves a medium number of agents and that agents' pay-off functions have a discontinuous response to increased congestion. First we consider a single adaptive agent facing a stationary environment. We demonstrate that the simple learning rules proposed by Roth and Er'ev can be extremely sensitive to small changes in the initial conditions and that events early in a simulation can affect the performance of the rule over a relatively long time horizon. In contrast, a reinforcement learning rule based on standard practice in the computer science literature converges rapidly and robustly. The situation is reversed when multiple adaptive agents interact: the RE algorithms often converge rapidly to a stable average aggregate attendance despite the slow and erratic behavior of individual learners, while the CS based learners frequently over-attend in the early and intermediate terms. The symmetric mixed strategy equilibria is unstable: all three learning rules ultimately tend towards pure strategies or stabilize in the medium term at non-equilibrium probabilities of attendance. The brittleness of the algorithms in different contexts emphasize the importance of thorough and thoughtful examination of simulation-based results.

Bell, Ann Maria↗
NASA NTRS1992

A generalized gamma(s)-family of self-starting algorithms for computational structural dynamics

A generalized gamma(s)-family of self-starting single-step formulations are presented in order to provide simplified yet effective dynamic attributes to include features towards eliminating the need to involve accelerations in the computational process for structural dynamic problems. By appropriately selecting the parameters pertaining to gamma(s)(s = 1, 2, 3), both explicit and implicit formulations are obtained. The stability and accuracy characteristics of the gamma(s)-family of representations are presented to validate the robustness of the formulations for structural dynamic problems. Numerous illustrative examples are described and the results are in excellent agreement and validate the applicability of these formulations for structural dynamic computations.

Namburu, Raju R.↗
NASA NTRS1986

Reduced conservatism in stability robustness bounds by state transformation

This note addresses the issue of 'conservatism' in the time domain stability robustness bounds obtained by the Liapunov approach. A state transformation is employed to improve the upper bounds on the linear time-varying perturbation of an asymptotically stable linear time-invariant system for robust stability. This improvement is due to the variance of the conservatism of the Liapunov approach with respect to the basis of the vector space in which the Liapunov function is constructed. Improved bounds are obtained, using a transformation, on elemental and vector norms of perturbations (i.e., structured perturbations) as well as on a matrix norm of perturbations (i.e., unstructured perturbations). For the case of a diagonal transformation, an algorithm is proposed to find the 'optimal' transformation. Several examples are presented to illustrate the proposed analysis.

Yedavalli, R. K.↗
NASA NTRS1991

The pulse-pair algorithm as a robust estimator of turbulent weather spectral parameters using airborne pulse Doppler radar

The pulse pair method for spectrum parameter estimation is commonly used in pulse Doppler weather radar signal processing since it is economical to implement and can be shown to be a maximum likelihood estimator. With the use of airborne weather radar for windshear detection, the turbulent weather and strong ground clutter return spectrum differs from that assumed in its derivation, so the performance robustness of the pulse pair technique must be understood. Here, the effect of radar system pulse to pulse phase jitter and signal spectrum skew on the pulse pair algorithm performance is discussed. Phase jitter effect may be significant when the weather return signal to clutter ratio is very low and clutter rejection filtering is attempted. The analysis can be used to develop design specifications for airborne radar system phase stability. It is also shown that the weather return spectrum skew can cause a significant bias in the pulse pair mean windspeed estimates, and that the poly pulse pair algorithm can reduce this bias. It is suggested that use of a spectrum mode estimator may be more appropriate in characterizing the windspeed within a radar range resolution cell for detection of hazardous windspeed gradients.

Baxa, Ernest G., Jr.↗
NASA NTRS1992

A comparison of force control algorithms for robots in contact with flexible environments

In order to perform useful tasks, the robot end-effector must come into contact with its environment. For such tasks, force feedback is frequently used to control the interaction forces. Control of these forces is complicated by the fact that the flexibility of the environment affects the stability of the force control algorithm. Because of the wide variety of different materials present in everyday environments, it is necessary to gain an understanding of how environmental flexibility affects the stability of force control algorithms. This report presents the theory and experimental results of two force control algorithms: Position Accommodation Control and Direct Force Servoing. The implementation of each of these algorithms on a two-arm robotic test bed located in the Center for Intelligent Robotic Systems for Space Exploration (CIRSSE) is discussed in detail. The behavior of each algorithm when contacting materials of different flexibility is experimentally determined. In addition, several robustness improvements to the Direct Force Servoing algorithm are suggested and experimentally verified. Finally, a qualitative comparison of the force control algorithms is provided, along with a description of a general tuning process for each control method.

Wilfinger, Lee S.↗
NASA NTRS2005

A First and Second Order Moment Approach to Probabilistic Control Synthesis

This paper presents a robust control design methodology based on the estimation of the first two order moments of the random variables and processes that describe the controlled response. Synthesis is performed by solving an multi-objective optimization problem where stability and performance requirements in time- and frequency domains are integrated. The use of the first two order moments allows for the efficient estimation of the cost function thus for a faster synthesis algorithm. While reliability requirements are taken into account by using bounds to failure probabilities, requirements related to undesirable variability are implemented by quantifying the concentration of the random outcome about a deterministic target. The Hammersley Sequence Sampling and the First- and Second-Moment- Second-Order approximations are used to estimate the moments, whose accuracy and associated computational complexity are compared numerically. Examples using output-feedback and full-state feedback with state estimation are used to demonstrate the ideas proposed.

Crespo, Luis G.↗
NASA NTRS2012

Multi-Angle Implementation of Atmospheric Correction for MODIS (MAIAC). Part 3: Atmospheric Correction

This paper describes the atmospheric correction (AC) component of the Multi-Angle Implementation of Atmospheric Correction algorithm (MAIAC) which introduces a new way to compute parameters of the Ross-Thick Li-Sparse (RTLS) Bi-directional reflectance distribution function (BRDF), spectral surface albedo and bidirectional reflectance factors (BRF) from satellite measurements obtained by the Moderate Resolution Imaging Spectroradiometer (MODIS). MAIAC uses a time series and spatial analysis for cloud detection, aerosol retrievals and atmospheric correction. It implements a moving window of up to 16 days of MODIS data gridded to 1 km resolution in a selected projection. The RTLS parameters are computed directly by fitting the cloud-free MODIS top of atmosphere (TOA) reflectance data stored in the processing queue. The RTLS retrieval is applied when the land surface is stable or changes slowly. In case of rapid or large magnitude change (as for instance caused by disturbance), MAIAC follows the MODIS operational BRDF/albedo algorithm and uses a scaling approach where the BRDF shape is assumed stable but its magnitude is adjusted based on the latest single measurement. To assess the stability of the surface, MAIAC features a change detection algorithm which analyzes relative change of reflectance in the Red and NIR bands during the accumulation period. To adjust for the reflectance variability with the sun-observer geometry and allow comparison among different days (view geometries), the BRFs are normalized to the fixed view geometry using the RTLS model. An empirical analysis of MODIS data suggests that the RTLS inversion remains robust when the relative change of geometry-normalized reflectance stays below 15%. This first of two papers introduces the algorithm, a second, companion paper illustrates its potential by analyzing MODIS data over a tropical rainforest and assessing errors and uncertainties of MAIAC compared to conventional MODIS products.

Lyapustin, A.↗
NASA NTRS1992

Convexity property of the one-sided multivariable stability margin

In evaluating the stability robustness of multivariable control systems having one-sided parameter uncertainty, a problem that naturally arises is the minimization over diagonal matrices D of the greatest eigenvalue of (e sup D Ae sup -D + (e sup D Ae sup -D)*)/2. The minimization is proved to be convex, thus guaranteeing that every local minimum is also a global minimum and, in theory, guaranteeing the global convergence of generalized gradient nonlinear programming algorithms for computing the minimizing D.

Tekawy, Jonathan A.↗
NASA NTRS2003

Aeroservoelastic Model Validation and Test Data Analysis of the F/A-18 Active Aeroelastic Wing

Model validation and flight test data analysis require careful consideration of the effects of uncertainty, noise, and nonlinearity. Uncertainty prevails in the data analysis techniques and results in a composite model uncertainty from unmodeled dynamics, assumptions and mechanics of the estimation procedures, noise, and nonlinearity. A fundamental requirement for reliable and robust model development is an attempt to account for each of these sources of error, in particular, for model validation, robust stability prediction, and flight control system development. This paper is concerned with data processing procedures for uncertainty reduction in model validation for stability estimation and nonlinear identification. F/A-18 Active Aeroelastic Wing (AAW) aircraft data is used to demonstrate signal representation effects on uncertain model development, stability estimation, and nonlinear identification. Data is decomposed using adaptive orthonormal best-basis and wavelet-basis signal decompositions for signal denoising into linear and nonlinear identification algorithms. Nonlinear identification from a wavelet-based Volterra kernel procedure is used to extract nonlinear dynamics from aeroelastic responses, and to assist model development and uncertainty reduction for model validation and stability prediction by removing a class of nonlinearity from the uncertainty.

Brenner, Martin J.↗
NASA NTRS2004

Development and Evaluation of Fault-Tolerant Flight Control Systems

The research is concerned with developing a new approach to enhancing fault tolerance of flight control systems. The original motivation for fault-tolerant control comes from the need for safe operation of control elements (e.g. actuators) in the event of hardware failures in high reliability systems. One such example is modem space vehicle subjected to actuator/sensor impairments. A major task in flight control is to revise the control policy to balance impairment detectability and to achieve sufficient robustness. This involves careful selection of types and parameters of the controllers and the impairment detecting filters used. It also involves a decision, upon the identification of some failures, on whether and how a control reconfiguration should take place in order to maintain a certain system performance level. In this project new flight dynamic model under uncertain flight conditions is considered, in which the effects of both ramp and jump faults are reflected. Stabilization algorithms based on neural network and adaptive method are derived. The control algorithms are shown to be effective in dealing with uncertain dynamics due to external disturbances and unpredictable faults. The overall strategy is easy to set up and the computation involved is much less as compared with other strategies. Computer simulation software is developed. A serious of simulation studies have been conducted with varying flight conditions.

Song, Yong D.↗
NASA NTRS1989

Distributed neural control of a hexapod walking vehicle

There has been a long standing interest in the design of controllers for multilegged vehicles. The approach is to apply distributed control to this problem, rather than using parallel computing of a centralized algorithm. Researchers describe a distributed neural network controller for hexapod locomotion which is based on the neural control of locomotion in insects. The model considers the simplified kinematics with two degrees of freedom per leg, but the model includes the static stability constraint. Through simulation, it is demonstrated that this controller can generate a continuous range of statically stable gaits at different speeds by varying a single control parameter. In addition, the controller is extremely robust, and can continue the function even after several of its elements have been disabled. Researchers are building a small hexapod robot whose locomotion will be controlled by this network. Researchers intend to extend their model to the dynamic control of legs with more than two degrees of freedom by using data on the control of multisegmented insect legs. Another immediate application of this neural control approach is also exhibited in biology: the escape reflex. Advanced robots are being equipped with tactile sensing and machine vision so that the sensory inputs to the robot controller are vast and complex. Neural networks are ideal for a lower level safety reflex controller because of their extremely fast response time. The combination of robotics, computer modeling, and neurobiology has been remarkably fruitful, and is likely to lead to deeper insights into the problems of real time sensorimotor control.

Beer, R. D.↗